<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div dir="auto" style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">皆様<div class=""><br class=""></div><div class="">下記の通りセミナーのご案内をさせていただきます．</div><div class=""><br class=""></div><div class="">岡数学研究所</div><div class="">森本 徹</div><div class=""><br class=""></div><div class=""><br class=""></div><div class=""><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class="">Seminar in Oka Mathematical Institute </div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans"; min-height: 45px;" class=""><br class=""></div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class="">Date: September 25 Monday, 2023</div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class="">Place: Oka Mathematical Institute, Nara Women's University</div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans"; min-height: 45px;" class=""><br class=""></div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class="">Speakers and Titles</div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans"; min-height: 45px;" class=""><br class=""></div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class="">10:30-11:30 Boris Doubrov( Belarus State University)</div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class=""> Equivalence of bracket-generating vector distributions via control theory</div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans"; min-height: 45px;" class=""> <br class="webkit-block-placeholder"></div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class=""> 13:30-14:30 Toshihisa Kubo( Ryukoku University)</div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class=""> On the equivariant differential operators for SL(3,R) with maximal parabolic subgroup</div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans"; min-height: 45px;" class=""><br class=""></div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class=""> 15:00-16:00 Masanori Adachi(Shizuoka University)</div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class=""> TBA</div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans"; min-height: 45px;" class=""> <br class="webkit-block-placeholder"></div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class=""> %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% </div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans"; min-height: 45px;" class=""> <br class="webkit-block-placeholder"></div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class="">Titles and Abstracts</div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans"; min-height: 45px;" class=""><br class=""></div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class=""> B.Doubrov</div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class="">Title: Equivalence of bracket-generating vector distributions via control theory</div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class="">Abstract: We canonically associate a pseudo-product structure with any bracket-generating distribution. Under some additional non-degeneracy conditions one can use the linearization principle and study these structures via systems of linear ODEs whose solution space possesses an invariant symplectic form.</div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans"; min-height: 45px;" class=""> <br class="webkit-block-placeholder"></div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class="">The symbol of such linear systems is described by a homogeneous element of degree -1 in the Lie algebra sp(2n,R) equipped with an arbitrary parabolic grading. We show how such elements can be effectively classified.</div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans"; min-height: 45px;" class=""> <br class="webkit-block-placeholder"></div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class="">In case of (2,3,5) distributions this construction leads to a pseudo-product structure modeled by the parabolic homogeneous space G_2/B where B is the Borel subgroup.</div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans"; min-height: 45px;" class=""><br class=""></div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans"; min-height: 45px;" class=""><br class=""></div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class="">％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％</div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans"; min-height: 45px;" class=""><br class=""></div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class="">T.Kubo</div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans"; min-height: 45px;" class=""><br class=""></div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class=""> Title: On the equivariant differential operators for SL(3,R) with maximal parabolic subgroup</div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class=""> Abstract: Let $G \supset P$ be a real simple Lie group and a parabolic subgroup, respectively. For finite dimensional representations $V_i$ ($i=1,2$) of $P$, let $\mathcal{V}_i \to G/P$ denote the $G$-equivariant homogeneous vector bundle $\mathcal{V}_i$ over $G/P$ with fiber $V_i$. Differential operators $\mathcal{D}\colon C^\infty(G/P, \mathcal{V}_1) \to C^\infty(G/P, \mathcal{V}_2)$ are said to be \emph{equivariant} (or \emph{covariant} or \emph{intertwining}) if $\mathcal{D}$ is equivariant under the actions of $G$ on $C^\infty(G/P, \mathcal{V}_i)$ $(i=1,2)$. A classical example of such an operator is the wave operator $\square_{3,1}$ on the Minkowski space $\mathbb{R}^{3,1}$ of signature $(3,1)$. Equivariant differential operators are important objects in both representation theory and parabolic geometry.</div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans"; min-height: 45px;" class=""> <br class="webkit-block-placeholder"></div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class="">In this talk we shall discuss a classification and explicit construction of equivariant differential operators for the following setting:</div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class="">\begin{equation*}</div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class="">(G,P; V_1, V_2) = (SL(3,\mathbb{R}), P_{1,2}; F_n, F_m).</div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class="">\end{equation*}</div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class="">Here, $P_{1,2}$ is the maximal parabolic subgroup corresponding to the partition $(1,2)$, and $F_n$ (resp.\ $F_m$) is the finite dimensional irreducible representation of $P_{1,2}$ of dimension $n$ (resp.\ $m$). This is based on joint work in progress with Bent Orsted.</div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans"; min-height: 45px;" class=""> <br class="webkit-block-placeholder"></div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans";" class="">％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％</div><div style="margin: 0px; font-stretch: normal; font-size: 30px; line-height: normal; font-family: "Hiragino Sans"; min-height: 45px;" class=""><br class=""></div></div></div></body></html>